Month: November 2013

What Have I Gotten Myself Into?

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I have posted previously that I am teaching 1 section of Calculus and 8 heterogeneous sections (4 each day) of Math AIS.  I am personally hitting the wall in Math AIS.  Here are my thoughts:

  • I like the students.
  • I like that I can pick and choose what I do (or don’t do) in the class.
  • I like that I don’t have to “grade” the students.
  • I dislike that there isn’t a grade or any extrinsic motivation for them to do ANYTHING in Math AIS.
  • I dislike that because I am creative and unwilling to bow down to drill and kill that Math AIS is eating up all of my plan time for Calculus.
  • I dislike that the classes are VERY heterogeneous and that I don’t feel I am doing any population well. (On paper, I have mostly Algebra 1 and Fundamentals of Algebra.  In reality I have students from 2 different Algebra 1 teachers and 3 different Fundamentals of Algebra teachers.  So they are all at different places in the curriculum.  Then I also have 5 Geometry and 2 Algebra 2 students thrown in the mix.  Sink or swim, suckahs!!)
  • I dislike that I have nothing to “follow”…no curriculum, no end goals….just go in and teach your angle-sinde-angle off…
  • I dislike that I don’t have anyone to collaborate with in my building…to bounce ideas off of…to build this course.
  • I like the idea of flipping the classroom a bit….
  • I dislike knowing that I don’t even have any real idea of how to start to do that or what it would like…
  • I like to see students “doing” math.
  • I like to seeing students doing relevant math and making connections.
  • I like to see students “get it”.

So….there are my thoughts as they stand right now.  I had a long talk with my content specialist over lunch today and discussed these thoughts.  He listened, but he doesn’t really have an answer. (Not that I really expected one.)  Is there anyone else out there who is teaching Math AIS? Particularly with mixed classes?  If you do, or know someone who does, could you pass this post on to them?  Thanks!

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Finding Patterns

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At the end of last class I gave my students the preassessment for the Manipulating Polynomials lesson on the Math Assessment Project website.  I had ONE student even come close to understanding the essence of the problems.  Today I taught the associated mini-lesson.  I was  a little worried, but I trusted the process and jumped in with both feet.

I gave them one extra example, broke them into groups, and had them work on the cut-and-paste-poster activity.  I asked the students who were struggling to take one of the dot patterns and start by just writing down the number of black dots, white dots, and total dots.  Then we discussed how the number of each type of dot could be expressed as a function of n (not using that terminology, but you know what I mean).  There was some struggling.  There was some fussing.  There were even a couple of complaints of, “When am I ever going to use this?”   (More on this below) The satisfying part, though, is that they KEPT WORKING.  They worked through their struggles.  They asked for help when they needed it. (I admit, I broke down and gave them the formula to find the nth perfect square and nth triangular number.)  They discussed the problems with their peers.  They even seemed satisfied when they arrived at a solution.

I have worked very hard this year trying to have my AIS students see beyond the tricks and gimmicks that they may learn in class and to enjoy the rigor and perseverence of math.  This was one of the first times that they showed me that they were willing and able to reason mathematically.  They showed that eventhough the problem was challenging for them, they were willing to think analytically and to persevere.

Looking back, I think this task was successful for many reasons, but mostly because of the relevance of the task. Not the “real world relevance”, but the relavance quoted from Ben Blum-Smith on Dan Meyer’s blog:

The real test of whether a math problem is “relevant” is not “do you use this in ‘real life’,” whatever that means, but “do you want to solve it?” It’s not that you want to solve it because it’s relevant; wanting to solve it is what it means to be relevant.

These students were genuinely interested on some level.  I think that they were intrigued that they could find an expression that could describe what was happening in the picture.  They were excited that this even allowed them to find future values beyond what was on the paper in front of them.  This was empowering to see in a class room of students who dislike and have ven come to fear math.  I am definitely looking forward to finding more and more relevant tasks for my Math AIS students.

Side Note:  Speaking of relevance….I think a surefire way to decide if a task has lost it’s relevance is when a student asks, “When are we ever going to use this?”  This means that a student sees no connection to anything they could possibly ever do in the “real world”.  I have taken two distinctly different paths when being asked this question.  First, I have scrapped the activity and done something new.  When I do this I usually see that there is some underlying skill that they are struggling with.  Once this is remedied, the task at hand usually seems much more
“doable”.  Secondly, I have honest and frank discussions about what the student(s) want to do in life.  What are their goals, dreams, and aspirations.  Once they can remove themselves from the now and look at the bigger picture they realize that the tasks we are looking are appropriate.  Not to mention that it might be beneficial to practice and become efficient in the skills of rigor and perseverence.

Project Based Learning

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First of all, I must reiterate that I teach mostly Math AIS all day. I have a little less stress of having to “get through” everything so I can take my time and let students tinker and even, at times, flounder. Also, my classes are small…10 student max. Here is what happened today with my Fundamentals of Algebra students:

I presented my students with a tape measure (the wind-up kind). I posted the following task to the students:

You need to turn the handle of the tape measure at exactly 1 mile per hour. (That is prove it to me that you are indeed moving the handle at exactly 1 mile per hour.)

I took this lesson from Jonathan. He took it a lot further and did angular velocity and all sorts of other cool stuff. My students have been doing ratios, proportions, and unit conversions so I was perfectly happy letting them just find out how to turn the handle in order for the it to be moving at a speed of 1 mile per hour.

My morning classes struggled. For starters, they had NO IDEA how many feet are in a mile (one student volunteered an answer of “12” when asked how many feet are in a mile). More alarmingly is that they had no idea where to start. I had to lead them through this activity way more than I wanted or that I should have had to. I reevaluated and over lunch I made this. I realized that whether I liked it or not, the students need some scaffolding to work more independently. Some of this has to do with the fact that this population is just not very strong at working independently. A lot of it has to do with that when these students are taught unit conversions and proportions nothing is put into context for them (and much of anything else for that matter. This is a constant battle for me. My students are mostly taught an algorithm and then told to apply it. There is very little thinking involved. More on this in another post.

My one period after lunch is my “rough” class. They struggled. Again. However, I do believe that they struggled less than if I had given them the same un-scaffolded assignment that I gave my morning classes.

Note: My AIS periods alternate every other day. I wrote the first part of this after Day One. Here is the recap of today.

I used the scaffolding with my classes again today. It went about the same as last period yesterday. I think they got it better than without the scaffolding, but I just don’t know.  These AIS classes are just so hard to read.  Twelve weeks in and I still am struggling with this.  I think part of the problem is that these students have years and years of experience of faking it.  That is, they have perfected the craft of saying the right things and going through the right motions to make me think that they have it even when I lost them 17 lessons ago.  Over the last eleven years of teaching Algebra 2 with Trigonometry, I learned to identify these students.  I am starting to realize though, that maybe it was not so much that I was good at identifying them as they were better at asking for help.  Perhaps they were even less afraid of admitting they had a question or that they were falling behind.  They didn’t view this as a weakness, but a challenge that they had to overcome. 

I loved the context and ambiguity of this activity. I think it was perfect for an AIS class and it fit into the context of what is currently being taught in their math class right now.  I am not sure how it was received.  I think there was a slight heightened level of curiosity, but I still need to work on inspiring a higher level of work ethic.  Time to find another task for another day…

Out With the Old??

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Wow, I can’t believe it has been so long since I last posted something. I have recently started getting back into reading blogs and getting really excited about all of the great math teaching that is going on out there. I am dedicating myself to write one blog post a week until the New Year. Here goes number one….”

I have recently come to the conclusion that some people are never going to change the way they teach. Standards may change, district goals may change, curricula may change…they will still teach basically the same stuff the same way that they always have. Usually, they teach it the same way they learned it in school. I do NOT claim to be an expert, but I do know that I challenge my students to think. I try new things all of the time. I get really excited when I find a new and engaging way to teach something. My students get frustrated because I refuse to give them the answer. I implore my students to find the joy in the process and not just getting the right answer. I believe that anyone can learn mathematics, but some students lack the perseverance and dedication to even try. I wake up in the middle of the night trying to figure out new ways to connect to these students. And this is the reason that I get frustrated with the teachers who stand in front of the class and lecture the same notes, the same way that they did last year…and the year before that. Sure, they may provide “guided notes”…and do review games of some sort or another occasionally, but the actual instruction is the same as it has always been. This is also the reason, however, that I am back on here. I am back on here so that I hold myself responsible to my blogging community to keep creating lessons in which my students are challenged to think; to actually do math. Furthermore, I am here to get inspired (and to steal ideas) from the amazing teachers that I follow on here. I can’t wait!